XAT Algebra Questions 2027: Important Topics, Solved Questions and Preparation Tips
Algebra is an important part of the Quantitative Aptitude and Data Interpretation section of XAT. The best way to prepare for XAT algebra questions 2027 is to combine strong fundamentals with practice in equations, inequalities, progressions, logarithms, exponents, functions and algebraic identities.
The official XAT exam pattern includes algebra among the mathematical areas assessed in the Quantitative Aptitude and Data Interpretation section. However, XLRI does not prescribe a fixed algebra-only question count. Candidates should therefore prepare recurring concepts instead of relying on a predicted weightage.
Reviewed by Kaushik Kapoor — Co-founder and Director of Erudite, a premium MBA entrance coaching institute headquartered in Kolkata. An alumnus of XLRI Jamshedpur and St. Xavier’s College, Kolkata, he has over 25 years of experience in student mentoring, MBA entrance preparation, test-prep strategy and academic training.
How Important Is Algebra in XAT 2027?
Algebra is important because it tests more than direct calculation. A typical question may require you to:
- Translate a condition into an equation
- Identify restrictions on a variable
- Compare possible solution ranges
- Use an identity instead of lengthy expansion
- Combine two concepts, such as logarithms and quadratic equations
- Reject an algebraic root that is outside the permitted domain
The exact number of algebra questions can change from year to year. Official previous-year papers are therefore more useful than fixed weightage predictions when evaluating recurring question types.
Important XAT Algebra Topics for 2027
| Priority | Topic | What to Prepare | Common Trap |
|---|---|---|---|
| High | Linear and simultaneous equations | Substitution, elimination, ratios and word-based equations | Creating the wrong equation from the condition |
| High | Quadratic equations | Roots, discriminant, Vieta’s relations, common roots and parameter questions | Ignoring the condition for real roots |
| High | Inequalities and modulus | Critical points, interval testing and integer solutions | Reversing an inequality incorrectly |
| High | Sequences and series | AP, GP, sums, missing terms and algebraic patterns | Treating the common difference as automatically positive |
| High | Logarithms and exponents | Laws, domain restrictions and equation solving | Accepting roots outside the logarithmic domain |
| Medium–High | Algebraic identities | Factorisation, symmetric expressions and substitutions | Expanding when a direct identity is faster |
| Medium | Functions | Function values, compositions, domains and simple graphs | Confusing (f(a+b)) with (f(a)+f(b)) |
| Medium | Polynomials | Factors, remainders, roots and coefficients | Forgetting the remainder theorem |
| Medium | Surds and indices | Simplification and rationalisation | Applying exponent rules across addition |
| Medium | Maximum and minimum values | Quadratics, squares and inequality-based methods | Ignoring the permitted domain |
Essential Algebra Formulas for XAT
Quadratic Equations
For:
Ax^2+Bx+C=0
the roots are:
x=\frac{-B\pm\sqrt{B^2-4AC}}{2A}
If the roots are (\alpha) and (\beta):
\alpha+\beta=-\frac{B}{A}
\alpha\beta=\frac{C}{A}
The equation has real roots when:
B^2-4AC\geq 0
Common Algebraic Identities
(a+b)^2=a^2+b^2+2ab
(a-b)^2=a^2+b^2-2ab
a^2-b^2=(a-b)(a+b)
a^3+b^3=(a+b)(a^2-ab+b^2)
a^3-b^3=(a-b)(a^2+ab+b^2)
Arithmetic Progression
a_n=a+(n-1)d
S_n=\frac{n}{2}[2a+(n-1)d]
Geometric Progression
a_n=ar^{n-1}
For (r\neq1):
S_n=\frac{a(r^n-1)}{r-1}
Logarithms
\log_b(MN)=\log_b M+\log_b N
\log_b\left(\frac{M}{N}\right)=\log_b M-\log_b N
\log_b(M^k)=k\log_b M
For a real logarithm:
b>0,\quad b\neq1,\quad M>0
Modulus
For (B\geq0):
|A|\leq B \iff -B\leq A\leq B
|A|\geq B \iff A\leq-B\ \text{or}\ A\geq B
XAT Algebra Practice Questions with Step-by-Step Solutions
-
Question 1: Quadratic Equations and Roots
A quadratic equation has roots (a) and (b). If
x^2-12x+(k+2)=0
has real roots and
a^2+b^2=94,
find (k).
Solution
From the equation:
a+b=12
and:
ab=k+2
Use:
(a+b)^2=a^2+b^2+2ab
Substituting the known values:
12^2=94+2(k+2)
144=94+2k+4
46=2k
k=23
Check the real-root condition:
D=(-12)^2-4(1)(25)=144-100=44>0
Therefore, the equation has real roots.
Answer: (23)
-
Question 2: Arithmetic Progression
The first three terms of an arithmetic progression are positive. Their sum is 33, and the product of the first and third terms exceeds the second term by 29. Find the positive common difference.
Solution
Represent the three terms as:
a-d,\quad a,\quad a+d
Their sum is:
(a-d)+a+(a+d)=3a=33
Therefore:
a=11
The product of the first and third terms is:
(a-d)(a+d)=a^2-d^2
It exceeds the second term by 29:
a^2-d^2=a+29
Substitute (a=11):
121-d^2=40
d^2=81
d=\pm9
Because the question asks for the positive common difference:
d=9
The terms are (2,11,20), all of which are positive.
Answer: (9)
-
Question 3: Logarithmic Equation
Find the sum of all real values of (x) satisfying:
\log_2(x-1)+\log_2(x+3)=5
Solution
First determine the domain:
x-1>0
x+3>0
Together, these conditions give:
x>1
Apply the product rule:
\log_2[(x-1)(x+3)]=5
Convert to exponential form:
(x-1)(x+3)=2^5
x^2+2x-3=32
x^2+2x-35=0
Factorise:
(x+7)(x-5)=0
The possible roots are:
x=-7,\quad x=5
The root (-7) does not satisfy (x>1).
Therefore, the only valid value is:
x=5
Answer: (5)
-
Question 4: Absolute Value and Integral Solutions
Find the number of integral values of (x) satisfying:
|2x-5|\leq9
Solution
Using the modulus property:
-9\leq2x-5\leq9
Add 5 throughout:
-4\leq2x\leq14
Divide by 2:
-2\leq x\leq7
The integral values are:
-2,-1,0,1,2,3,4,5,6,7
There are 10 such values.
Answer: (10)
-
Question 5: Exponential Equation
Solve:
3^{x+1}+3^x=108
Solution
Write (3^{x+1}) as (3\cdot3^x):
3\cdot3^x+3^x=108
Factorise:
4\cdot3^x=108
3^x=27
Since:
27=3^3,
we get:
x=3
Answer: (3)
-
Question 6: Functions
If:
f(x)=x^2-2x,
find:
f(a+1)-f(a)
Solution
First calculate (f(a+1)):
f(a+1)=(a+1)^2-2(a+1)
=a^2+2a+1-2a-2
=a^2-1
Also:
f(a)=a^2-2a
Therefore:
f(a+1)-f(a)
=(a^2-1)-(a^2-2a)
=2a-1
Answer: (2a-1)
Additional XAT Algebra Practice Questions
Try these questions before checking the answer key.
-
Practice Question 1
If:
2x+3y=19
and:
x-y=2,
find (x+y).
-
Practice Question 2
If:
x+\frac{1}{x}=3,
find:
x^2+\frac{1}{x^2}
-
Practice Question 3
Find the remainder when:
p(x)=x^3-4x^2+x+6
is divided by (x-2).
-
Practice Question 4
A geometric progression has first term 3 and common ratio 2. Find the sum of its first five terms.
-
Practice Question 5
Find the number of integral values of (x) satisfying:
|3x-2|<10
Answer Key
- 8
- 7
- 0
- 93
- 6
How to Prepare for XAT Algebra
Week 1: Build the Foundations
Revise:
- Algebraic identities
- Factorisation
- Linear equations
- Quadratic equations
- Exponent rules
Solve straightforward questions until you can identify the applicable formula without hesitation.
Week 2: Work on Ranges and Restrictions
Study:
- Inequalities
- Absolute values
- Logarithmic domains
- Surds
- Integer-value conditions
After every solution, ask:
- Was any value excluded?
- Did I divide by a negative expression?
- Does the answer satisfy the original equation?
- Is the logarithm or denominator defined?
Week 3: Practise Applications and Mixed Concepts
Work on:
- AP and GP
- Functions
- Polynomials
- Parameter-based equations
- Questions combining two algebra topics
Maintain an error log with separate labels for:
- Concept errors
- Calculation errors
- Domain errors
- Misreading
- Poor question selection
Week 4: Use Timed Tests and Previous Papers
Complete:
- Topic-wise algebra tests
- QA-DI sectional tests
- Official XAT previous-year questions
- Full-length mock examinations
Timed practice helps you identify questions that should be attempted immediately and those that should be left for a later pass.
Expert Tips for Solving XAT Algebra Questions
Check the Domain Before Solving
In logarithm, rational-expression and square-root questions, write the domain before manipulating the equation. This prevents invalid roots from entering the final answer.
Use Options Strategically
When the answer choices are numerical, substitution can be faster than deriving a complete symbolic solution. Use it when the options are distinct and easy to test.
Look for Symmetry
Expressions involving:
x+\frac1x,\quad a+b,\quad ab,\quad a-d,\ a,\ a+d
often signal a standard identity or symmetric representation.
Do Not Assume a Sign
If:
d^2=81,
the mathematical conclusion is:
d=\pm9
Choose only one sign when the question supplies an additional condition such as (d>0).
Avoid Blind Expansion
Before expanding a large expression, check whether it matches:
- A difference of squares
- A perfect square
- A sum or difference of cubes
- A quadratic in another variable
Verify Parameter-Based Answers
When a question asks for a parameter such as (k), substitute the result into the original equation and verify any stated conditions, including real roots or positive values.
Common Mistakes to Avoid
- Forgetting the domain of a logarithm
- Dividing an inequality by a negative value without reversing the sign
- Accepting both algebraic roots without checking restrictions
- Assuming that a common difference or square root must be positive
- Expanding expressions that can be simplified through an identity
- Spending several minutes on a question that should be deferred
- Memorising formulas without practising when they apply
- Counting mixed-topic questions incorrectly during paper analysis
Frequently Asked Questions
How Many Algebra Questions Are Asked in XAT?
XLRI does not publish a fixed algebra-only question count. The official pattern provides an approximate total for the combined QA-DI section and identifies algebra as one of its constituent areas. The actual number of algebra and algebra-linked questions can vary by paper.
Which Algebra Topics Are Most Important for XAT 2027?
Begin with linear and quadratic equations, inequalities, modulus, logarithms, exponents, progressions and algebraic identities. Once these are stable, move to functions, polynomials, surds and maximum–minimum questions.
Is XAT Algebra More Difficult Than CAT Algebra?
The underlying concepts overlap substantially. XAT questions may feel difficult when they contain unusual conditions, domain restrictions or combinations of topics. Candidates preparing for both examinations should focus on concept transfer rather than maintaining completely separate formula lists.
How Should a Beginner Prepare for XAT Algebra?
Start with equations, identities and factorisation. Then study inequalities, logarithms and progressions. Complete short topic tests before moving to mixed sets and full sectionals. Accuracy should be established before introducing strict time limits.
Are Previous-Year Papers Enough for XAT Algebra Preparation?
Previous papers are essential for understanding question style and selection, but they are not sufficient on their own. They should be combined with concept revision, topic-wise exercises, timed sectionals and analysis of mistakes.
Final Preparation Advice
Strong XAT algebra performance comes from three habits: recognising the underlying structure, checking restrictions and selecting questions carefully. Build your foundations first, practise a range of question types and use official previous-year papers to understand how algebra appears within the broader QA-DI section.
During mocks, do not judge progress only by the number of questions attempted. Track accuracy, average time, avoidable errors and the number of questions correctly deferred. That analysis will produce a more reliable improvement in your XAT 2027 preparation.